Method for evaluating output signals of a rotational rate sensor unit and rotational rate sensor unit

ABSTRACT

A method for evaluating output signals of a rotational rate sensor unit, including providing an n-tuple of angular speed values measured by at least one rotational rate sensor of the rotational rate sensor unit, in a first step; determining an intermediate value as a function of the n-tuple of angular speed values, in a second step; calculating a new change of orientation value as a function of the intermediate value and an earlier change of orientation value stored in a register of the rotational rate sensor unit, in a third step; and storing the new change of orientation value in the register, in a fourth step, repeating the first, second, third, and fourth step until, the new change of orientation value is read out by an external data processing unit connected to the rotational rate sensor unit, and/or, an exceeding of a threshold value is detected.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a 371 patent application of PCT/EP2012/061657 filed Jun. 19,2012, which claims priority to German Patent Application No. 10 2011 081049.8 filed Aug. 16, 2011, both applications are expressly incorporatedby reference herein in their entireties.

FIELD

The present invention is based on a method for evaluating output signalsof a rotational rate sensor system, and on a rotational rate sensorsystem.

BACKGROUND INFORMATION

Rotational rate sensor systems are generally available. German PatentApplication No. DE 101 108 196 A1 describes a rotational rate sensorhaving Coriolis elements for measuring an angular speed, a first andsecond Coriolis element being connected to one another via a spring andbeing excited to oscillations parallel to a first axis, a first and asecond detection device detecting a deflection of the first and secondCoriolis element based on a Coriolis force acting on the Corioliselements, so that the difference between a first detection signal of thefirst detection device and a second detection signal of the seconddetection device is a function of the Coriolis force and is thereforealso a function of the momentary angular speed.

German Patent Application No. DE 10 2007 060 942 A1 describes amultichannel rotational rate sensor that is suitable for measuringrotational rates about axes of rotation oriented perpendicular to oneanother. In particular, three-channel rotational rate sensors or systemsof rotational rate sensors enable a measurement about three mutuallyindependent axes of rotation. Such rotational rate sensors, or systemsof rotational rate sensors, are used for example to determine theposition of a portable device such as a mobile telephone, a tabletcomputer, or the like, relative to a reference system. Here thecalculation of change of position takes place as a function of theangular changes measured by the rotational rate sensors and provided asoutput signal.

A method for calculating the change in position is found, for example,in U.S. Pat. No. 3,231,726 A. Because angular changes are notcommutative, it is necessary to read out the output signals of therotational rate sensors from the rotational rate sensor with a highsampling rate. This sampling rate has to be significantly higher thanthe frequency range in which the movements that are to be measured arefound. In this way, complex rotations (rotations about three axes) aredecomposed into many smaller rotations. For example, human movementstake place in the frequency range below 20 Hz. An error-free integrationof these signals typically requires a sampling rate of 100 Hz. Adisadvantage is that, due to the high sampling rates, the main processorof the portable device has to be active relatively frequently in orderto read out and further process the output signals of the rotationalrate sensors. This results in a comparatively high power consumption. Inparticular in portable devices, due to limited battery capacities, thisresults in reduction of the battery running time of the portable device.

SUMMARY

An example method according to the present invention and an examplerotational rate sensor unit according to the present invention may havethe advantage that the data transfer between the rotational rate sensorunit and the external data processing unit, as well as energyconsumption, are substantially reduced. In this way, the battery runningtime can preferably be substantially increased if the example methodaccording to the present invention is used for example in abattery-operated portable device. These advantages are achieved in thatthe output signals of the rotational rate sensor, or of the multiplicityof rotational rate sensors, are already prepared in a comparativelysimple manner in the rotational rate sensor unit by immediatelyconverting the angular speed values into the constantly updated newchange of orientation value, taking into account the earlier change oforientation value stored in the register. This new change of orientationvalue always contains the information about the last change of positionof the rotational rate sensor unit. The current change of orientationvalue is successively summed by multiple repetition of the loop of thefirst, second, third, and fourth method steps, so that all of the itemsof change of position information are represented in the current newchange of orientation value. The external data processing unit, forexample the main processor of the portable device, advantageouslyrequires only the one current change of orientation value in order toregister the changes in position that have taken place since the lastreading out. For this purpose, a substantially lower sampling rate isadequate, because all of the items of information occurring during aloop no longer have to be constantly queried. This means that a lowerquantity of data has to be transmitted and a longer dwell time of theexternal data processing unit in an energy-saving mode or sleep mode isenabled, thus lowering energy consumption, and in particular increasingthe battery running time of the portable device. In addition, the changeof orientation value is preferably monitored constantly orintermittently using a threshold monitoring unit, so that errors andimprecisions in the change of orientation value, resulting for examplefrom rounding errors or approximation calculations, can be reduced to apreselected maximum degree. In the fourth method step, the earlierchange of orientation value stored in the register is preferablyoverwritten during each loop with the new change of orientation value.The n-tuple of angular speeds preferably includes a single angular speedabout an axis of rotation (n=1) or three angular speeds about threeindependent axes of rotation (n=3). Given measurement in more than onespecial direction, the angular speed values are measured for exampleusing a single multichannel rotational rate sensor or a plurality ofsingle-channel rotational rate sensors. The rotational rate sensorspreferably include micromechanical rotational rate sensors on asemiconductor substrate that were produced in a semiconductor productionprocess. In an alternative specific embodiment, it is possible for eachnew orientation value in each loop to additionally also be stored in anoutput register, fashioned for example as an FIFO (first in first out)register, from which they can be read out successively, preferablycorresponding to the temporal sequence in which they were stored, by theexternal data processing unit.

Advantageous embodiments and developments of the present invention canbe learned from the description, with reference to the figures.

According to a preferred specific embodiment, it is provided that afterexecution of the fifth or sixth method step, in a seventh method stepthe change of orientation value stored in the register is set to anoriginal value and the method starts over with the first method step.The original value preferably includes a kind of null value, i.e., onein which no change of the orientation has taken place. Advantageously,after the resetting of the change of orientation value stored in theregister, errors that have arisen during the calculation of therespective change of orientation value no longer have an effect on thecalculation of the new change of orientation value in the followingloop. In this way, the maximum occurrence error can be limited. A changeof orientation value set to zero, expressed as a change of orientationvector in the form of a quaternion, means that no change of position hastaken place, and in particular is expressed as follows:

$q_{l,o} = \begin{pmatrix}1 \\0 \\0 \\0\end{pmatrix}$

According to a preferred specific embodiment, it is provided that thechange of orientation value includes a change of orientation vector, inparticular a quaternion. Advantageously, in this way a change ofposition in three-dimensional space can be represented and furtherprocessed comparatively easily. The use of a number system based onquaternions has the advantage that rotations in three-dimensional spacecan be represented and further processed particularly easily andefficiently. Each quaternion includes four scalar number values, so thatthe register is designed in particular for the storage of four valuesper loop.

According to a preferred specific embodiment, it is provided that in thesixth method step it is monitored whether the length of the change oforientation vector calculated in the third method step exceeds aconfigurable and/or prespecified threshold value. The change oforientation vector is intended to indicate only the change inorientation. For this purpose, the orientation vector should have lengthone (also as norm or magnitude of the vector), i.e. |{right arrow over(q)}|=1, where {right arrow over (q)} is the change of orientationvector in the form of the quaternion. A deviation of the magnitude ofthe change of orientation vector from one is possible through apreferably only approximated calculation of the intermediate value. Suchan error is added to itself with each loop of the first, second, third,and fourth method steps. This results in an errored calculation of thenew change of orientation value in the third method step.Advantageously, this effect is minimized by monitoring the length of thenew change of orientation value and comparing it with a configurableand/or prespecified threshold value. If the threshold value is exceeded,the earlier change of orientation value stored in the register isbuffered in the output register and/or is read out by the external dataprocessing unit, and is subsequently set to zero. It is also possiblefor an interrupt to be sent to the external data processing unit by therotational rate sensor unit, and/or for the new change of orientationvalue to again be read out by the external data processing unit orstored in the output register.

According to a preferred specific embodiment, it is provided that thenumber of third method steps carried out since the earlier change oforientation value stored in the register was last set to the originalvalue are counted by a counter, and in the sixth method step it ischecked whether the counter has exceeded a configurable and/orprespecified further threshold value. Due to a preferably onlyapproximate calculation of the intermediate value, the danger that thechange of orientation value has errors increases with each loop of thefirst, second, third, and fourth method steps. In addition, theindividual errors are compounded with each loop of the first, second,third, and fourth method steps.

A limitation of the maximum number of possible loops of first, second,third, and fourth method steps, without the interim resetting of theearlier change of orientation value stored in the register,advantageously ensures that the error is limited to an acceptablemaximum degree. As soon as the maximum possible number of loops has beenreached, the new change of orientation value is buffered in the outputregister, and/or is read out by the external data processing unit, andsubsequently the earlier change of orientation value stored in theregister is set to zero, so that the subsequently calculated change oforientation value does not build on earlier approximation errors. Inaddition, it is possible that an interrupt is sent to the external dataprocessing unit by the rotational rate sensor unit.

According to a preferred specific embodiment, it is provided that, if anexceeding of a threshold value is detected in the sixth method step,then in a ninth method step the new and/or the earlier orientation valueis stored in an output register that can be read out by the externaldata processing unit. This has the advantage that the change of positionis buffered in the output register before the earlier change oforientation value stored in the register is discarded by the resettingto the original value. In this way it is ensured that no valuesdescribing a change of position are lost. The output register can now beread out immediately or at a later time by the external data processingunit.

According to a preferred specific embodiment, it is provided that in thesecond method step the intermediate value is calculated as a linearfunction of the n-tuple of angular speed values. Advantageously, alinear function is substantially easier to implement, in particular inthe form of a circuit, i.e., in hardware, than is a trigonometricfunction, which is standardly used for the calculation of change oforientation vectors, preferably quaternions. In particular, theapproximation through a linear function takes place as follows:

$q_{l} = {\begin{pmatrix}{\cos\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)} \\{{\omega_{x}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}} \\{{\omega_{y}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}} \\{{\omega_{z}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}}\end{pmatrix} \approx \begin{pmatrix}{{1@\omega_{x}} \cdot {T/2}} \\{\omega_{y} \cdot {T/2}} \\{\omega_{z} \cdot {T/2}}\end{pmatrix}}$

Here, ω_(x, y, z) corresponds to the respective angular speed about thex, y, and z axes, while T is the sampling time (where T=1/data rate).The computing expense is advantageously substantially reduced by thisapproximation.

According to a preferred specific embodiment, it is provided that in thethird method step the change of orientation value is formed by amultiplication, in particular a quaternion multiplication, of theintermediate value by the earlier change of orientation value stored inthe register. The earlier change of orientation value is the change oforientation value calculated respectively in the previously executedloop of the first, second, third, and fourth method steps, and stored inthe register in the fourth method step of the preceding loop, or is thechange of orientation value reset to the original value. In each loop,such a previous change of orientation value is multiplied by theintermediate value determined in the second method step. The productcorresponds to a new change of orientation value that is again stored inthe register, so that in the next loop it in turn acts as the previouschange of orientation value. The changes of position are thussuccessively summed in each loop.

According to a preferred specific embodiment, it is provided that in theeighth method step a plurality of change of orientation values read outin fifth method steps are summed by the external data processing unit.Advantageously, in this way a comparatively simple calculation of theeffective change of orientation value by the external data processingunit is possible without requiring a high sampling rate for thispurpose. In addition, there is an increase in tolerance with regard tothe sampling times. The summation of the plurality of change oforientation values preferably takes place in accordance with thecondition |{right arrow over (q)}_(eff)|=1, through multiple normalizingof the effective change of orientation value.

A further subject matter of the present invention is a rotational ratesensor unit for carrying out a method for evaluating output signals,having at least one rotational rate sensor for determining an n-tuple ofangular speeds, an evaluation circuit for determining an intermediatevalue as a function of the n-tuple of angular speeds, and a register forstoring a change of orientation value, the evaluation circuit furtherbeing configured for the calculation of a new change of orientationvalue as a function of the intermediate value and as a function of anearlier change of orientation value stored in the register, and therotational rate sensor unit being fashioned such that the new change oforientation value can be read out by an external data processing unitconnected to the rotational rate sensor unit. Advantageously, therotational rate sensor unit according to the present invention has theregister in which each earlier change of orientation value calculated inan earlier loop is to be stored, so that in the following loop a newchange of orientation value, based on this earlier value, is to becalculated. On the one hand, in this way no sampling of the rotationalrate sensor unit with a comparatively high and energy-intensive samplingrate is necessary, and on the other hand it is nonetheless ensured thatno measurement values are lost. In addition, the required data transferis substantially reduced. The battery running time of a portable devicecan be substantially increased in this way.

According to a preferred specific embodiment, it is provided that theevaluation circuit is configured so that the earlier change oforientation value stored in the register is reset when the new change oforientation value is read out, a monitoring unit for monitoring thelength of the new change of orientation value realized as a change oforientation vector indicates an exceeding of a threshold, and/or acounter for counting the calculations of the new change of orientationvalue carried out by the evaluation circuit indicates a furtherexceeding of a threshold. In this way, the precision of the rotationalrate sensor unit is advantageously substantially increased.

According to a preferred specific embodiment, it is provided that therotational rate sensor preferably includes a three-channel rotationalrate sensor, and/or the evaluation circuit is implemented in anintegrated circuit in the form of an ASIC. Advantageously, animplementation of the evaluation circuit in hardware can be realized soas to be comparatively power-saving, and on a comparatively small wafersurface. In particular, in this way a preparation of the angular speedis enabled without a space-intensive, cost-intensive, andenergy-intensive processor or microcontroller (μc).

Exemplary embodiments of the present invention are shown in the figuresand are explained in more detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic view of a method according to a first specificembodiment of the present invention.

FIG. 2 shows a schematic view of a method according to a second specificembodiment of the present invention.

FIG. 3 shows a schematic view of a method according to a third specificembodiment of the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

In the various Figures, identical parts are provided with identicalreference characters, and are therefore in general only named ormentioned once.

FIG. 1 shows a schematic view of a method for evaluating output signalsof a rotational rate sensor unit 1 according to a first specificembodiment of the present invention. Rotational rate sensor unit 1 has arotational rate sensor that measures rotational rates or angular speedsω_(x), ω_(y), ω_(z) about an X-axis, a Y-axis, and a Z-axis, the X, Y,and Z axes being independent of one another.

In a first method step 10, a tuple of three angular speed values ω_(x),ω_(x), and ω_(x) is measured by the rotational rate sensor and provided.In a second method step 20, from the three angular speed values ω_(x),ω_(x), and ω_(x), and using sampling time T (which corresponds to 1/datarate), respective angular modifications ω_(x)·T, ω_(y)·T and ω_(z)·T arecalculated. As a function of angular modification ω_(x)·T, ω_(y)·T,ω_(z)·T, an intermediate value q_(l) is then calculated approximately inthe form of a quaternion (change of position quaternion) from the linearfunction

$q_{l} \approx \begin{pmatrix}{{1@\omega_{x}} \cdot {T/2}} \\{\omega_{y} \cdot {T/2}} \\{\omega_{z} \cdot {T/2}}\end{pmatrix}$

In a third method step 30, for the calculation of a new change oforientation value q_(neu), intermediate value q_(l) is multiplied by anearlier change of orientation value q_(alt) stored in a register ofrotational rate sensor unit 1, in the context of a quaternionmultiplication. Previous orientation value q_(alt) originates eitherfrom a preceding loop of first, second, third, and fourth method step10, 20, 30, 40, or was previously set to an original value q_(l, 0) inthe context of a seventh method step 70; in particular:

$q_{l,0} = \begin{pmatrix}1 \\0 \\0 \\0\end{pmatrix}$

In a following, fourth method step 40, change of orientation valueq_(neu), which was recalculated in third method step 30, is stored inthe register. Here, earlier change of orientation value q_(alt) isoverwritten. Subsequently, the loop of first, second, third, and fourthmethod step 10, 20, 30, 40 is restarted. In an intermediate query 50, ineach loop it is queried whether new angular speed values ω_(x), ω_(y),and ω_(z) have been provided by the rotational rate sensor. If newangular speed values ω_(x), ω_(y), and ω_(z) are present, i.e., anangular change was measurable by the rotational rate sensor (because amovement of rotational rate sensor unit 1 took place), then in thirdmethod step 30 new change of orientation value q_(neu) is calculated asa function of an intermediate value q_(l) that was recalculated insecond method step 20, and as a function of earlier change oforientation value q_(alt) (corresponding to new orientation valueq_(neu) calculated in the previous loop) stored in the register.

The loops of first, second, third, and fourth method steps 10, 20, 30,40 (and intermediate query 50) are repeated until, in a sixth methodstep 60, a counter reaches a further configurable and/or prespecifiedthreshold value. The counter counts the number of multiplicationscarried out in context of third method step 30. In other words, thecounter counts how often new change of orientation value q has beenrecalculated. Because with each new multiplication the size of thepossible error increases, the limitation to a maximum number of thirdmethod steps 30 via the further configurable and/or prespecifiedthreshold value limits the error. If, in sixth method step 60, it isdetected that the further configurable and/or prespecified thresholdvalue t has been reached, then, in a ninth method step 90, currentchange of orientation value a q_(neu) is stored in an output register,for example an FIFO storage device, and earlier change of orientationvalue q_(alt) stored in the register is subsequently, in a seventhmethod step 70, again set to original value q_(l, 0). Change oforientation value q_(neu) stored in the output storage device is readout by the external data processing unit, in particular a processor of aportable device, so that no value describing the change in position islost.

FIG. 2 shows a schematic view of a method according to a second specificembodiment of the present invention, the second specific embodimentbeing substantially identical to the first specific embodimentillustrated on the basis of FIG. 1; but, differing from the firstspecific embodiment, in the second specific embodiment the length of neworientation value q_(neu) is monitored in sixth method step 60. If thelength of change of orientation vector q_(neu) calculated in thirdmethod step 30 exceeds a configurable and/or prespecified thresholdvalue, then in a tenth method step 100 an interrupt signal is produced.Earlier change of orientation value gait is then, in seventh method step70, reset to the original value q_(l, 0). Current change of orientationvalue q_(neu) is optionally discarded, read out by the external dataprocessing unit, and/or stored in the output register, for example anFIFO storage device.

FIG. 3 shows a schematic view of a method according to a third specificembodiment of the present invention, the third specific embodiment beingsubstantially identical to the first specific embodiment illustrated onthe basis of FIG. 1; but, differing from the first specific embodiment,in the third specific embodiment the loops of first, second, third, andfourth method step 10, 20, 30, 40 (and intermediate step 50) arerepeated until, in a fifth method step 80, the external data processingunit reads out new change of orientation value a q_(neu), or a readingout by the external data processing unit is detected. Alternatively, itis also possible that here the earlier change of orientation valueq_(alt) stored in the register is read out by the external dataprocessing unit. The read-out change of orientation value q_(neu) nowrepresents all positional changes since the last reading out. After thereading out of change of orientation value earlier change of orientationvalue q_(alt) stored in the register is again set, in a seventh methodstep 70, to original value q_(l, 0). It is possible that, in an eighthmethod step, the external data processing unit is used to sum aplurality of change of orientation values q_(neu) ^(i), read out fromrotational rate sensor unit 1 in fifth method steps 80, within theexternal data processing unit to form an effective change of orientationvalue q_(eff).

What is claimed is:
 1. A method for evaluating output signals of arotational rate sensor unit, comprising: providing an n-tuple-of angularspeed values measured by at least one rotational rate sensor of therotational rate sensor unit, in a first method step; determining anintermediate value as a function of the n-tuple of angular speed values,in a second method step; calculating a new change of orientation valueas a function of the intermediate value and as a function of an earlierchange of orientation value stored in a register of the rotational ratesensor unit, in a third method step; and storing the new change oforientation value in the register, in a fourth method step; wherein thefirst, second, third, and fourth method steps are repeated until, atleast one of: i) in a fifth method step, the new change of orientationvalue is read out by an external data processing unit connected to therotational rate sensor unit, and ii) in a sixth method step, anexceeding of a threshold value is detected, and wherein a current changeof orientation value is successively summed by multiple repetition of aloop including the first, second, third, and fourth method steps, sothat all of the items of change of position information are representedin the new change of orientation value.
 2. The method as recited inclaim 1, wherein the earlier change of orientation value stored in theregister is set, in a seventh method step, to an original value, inwhich no change of the orientation has taken place, after execution ofthe fifth or sixth method step, and the method being restarted with thefirst method step.
 3. The method as recited in claim 1, wherein the newchange of orientation value includes a change of a quaternion.
 4. Themethod as recited in claim 1, wherein the sixth method step includesdetecting whether a length of the new change of orientation valuecalculated in the third method step exceeds at least one of aconfigurable threshold value and a prespecified threshold value.
 5. Themethod as recited in claim 1, wherein the sixth method step includescounting by a counter the number of third method steps carried out sincethe earlier change of orientation value stored in the register was lastset to an original value, in which no change of the orientation hastaken place, and detecting whether the counter exceeds at least one of aconfigurable further threshold value and a prespecified furtherthreshold value.
 6. The method as recited in claim 1, furthercomprising: storing at least one of the new and the earlier orientationvalue in an output register that can be read out by the external dataprocessing unit, the storage taking place if, in the sixth method step,an exceeding of a threshold is detected.
 7. The method as recited inclaim 1, wherein at least one of: i) in the second method step, theintermediate value is calculated as a linear function of the n-tuple ofangular speed values, and ii) in the third method step, the new changeof orientation value is calculated by a quaternion multiplication of theintermediate value by the earlier change of orientation value stored inthe register.
 8. The method as recited in claim 2, wherein a pluralityof change of orientation values read out from the rotational rate sensorunit in fifth method steps is summed, in an eighth method step, by theexternal data processing unit to form an effective change of orientationvalue.
 9. A rotational rate sensor unit, comprising: at least onerotational rate sensor to determine an n-tuple of angular speeds; anevaluation circuit to determine an intermediate value as a function ofthe n-tuple of angular speeds; and a register to store a change oforientation value; wherein the evaluation circuit further beingconfigured to calculate a new change of orientation value as a functionof the intermediate value and as a function of an earlier change oforientation value stored in the register, and the rotational rate sensorunit is fashioned in such a way that the new change of orientation valueis capable of being read out by an external data processing unitconnected to the rotational rate sensor unit, and wherein a currentchange of orientation value is successively summed by multiplerepetition of a loop including the first, second, third, and fourthmethod steps, so that all of the items of change of position informationare represented in the new change of orientation value.
 10. Therotational rate sensor unit as recited in claim 9, wherein theevaluation circuit is configured to reset the earlier change oforientation value stored in the register when the new change oforientation value is read out.
 11. The rotational rate sensor as recitedin claim 9, further comprising: a monitoring unit to monitor a length ofthe new change of orientation value realized as a change of orientationvector as indicating an exceeding of a threshold value.
 12. Therotational rate sensor unit as recited in claim 9, further comprising: acounter to count the calculations of the new change of orientation valuecarried out by the evaluation circuit to indicate an exceeding of athreshold value.
 13. The rotational rate sensor unit as recited in claim9, wherein the rotational rate sensor includes a three-channelrotational sensor.
 14. The rotational rate sensor unit as recited inclaim 9, wherein the evaluation circuit is an ASIC.
 15. The rotationalrate sensor unit as recited in claim 9, wherein the intermediate valueis calculated as a linear function of the n-tuple of angular speedvalues.
 16. The rotational rate sensor unit as recited in claim 9,wherein the intermediate value is calculated as a linear function of then-tuple of angular speed values, and wherein the approximation through alinear function is performed as follows: $q_{l} = {\begin{pmatrix}{\cos\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)} \\{{\omega_{x}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}} \\{{\omega_{y}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}} \\{{\omega_{z}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}}\end{pmatrix} \approx \begin{pmatrix}{{1@\omega_{x}} \cdot {T/2}} \\{\omega_{y} \cdot {T/2}} \\{\omega_{z} \cdot {T/2}}\end{pmatrix}}$ where, ω_(x,y,z) corresponds to the respective angularspeed about the x, y, and z axes, and where T is the sampling time,where T=1/data rate.
 17. The method as recited in claim 1, wherein inthe second method step the intermediate value is calculated as a linearfunction of the n-tuple of angular speed values.
 18. The method asrecited in claim 1, wherein in the second method step the intermediatevalue is calculated as a linear function of the n-tuple of angular speedvalues, and wherein the approximation through a linear function isperformed as follows: $q_{l} = {\begin{pmatrix}{\cos\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)} \\{{\omega_{x}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}} \\{{\omega_{y}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}} \\{{\omega_{z}/{\overset{->}{\omega}}} \cdot {\sin\left( {{\overset{->}{\omega}} \cdot {T/2}} \right)}}\end{pmatrix} \approx \begin{pmatrix}{{1@\omega_{x}} \cdot {T/2}} \\{\omega_{y} \cdot {T/2}} \\{\omega_{z} \cdot {T/2}}\end{pmatrix}}$ where, ω_(x,y,z) corresponds to the respective angularspeed about the x, y, and z axes, and where T is the sampling time,where T=1/data rate.
 19. The method as recited in claim 1, wherein thesampling rate is less than about 100 Hz.
 20. The rotational rate sensorunit as recited in claim 9, wherein the sampling rate is less than about100 Hz.